{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2ONIC6G3DJ7PS3KKMWIF6KLQR4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fe16c7ccd2d20049ac4590bbbafa284a5da06c8afd96a1e60081044ad2649241","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-23T09:42:13Z","title_canon_sha256":"2b78ac1fc9076faba45765c52fe5d1abb73d7345083a0ab43796ed3dec385d13"},"schema_version":"1.0","source":{"id":"1404.5763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5763","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5763v1","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5763","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"2ONIC6G3DJ7P","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2ONIC6G3DJ7PS3KK","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2ONIC6G3","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f63cc365fe2451405f1558a4e758300e55fb7eaa10fb88a9d3dbc3e03b757009","target":"graph","created_at":"2026-05-18T02:53:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In \\cite{Ku0}, the ambiguity index $a_{(G,O)}$ was introduced for each equipped finite group $(G,O)$. It is equal to the number of connected components of a Hurwitz space parametrizing coverings of a projective line with Galois group $G$ assuming that all local monodromies belong to conjugacy classes $O$ in $G$ and the number of branch points is greater than some constant. We prove in this article that the ambiguity index can be identified with the size of a generalization of so called Bogomolov multiplier (\\cite{Kun1}, see also \\cite{BO87}) and hence can be easily computed for many pairs $(G,","authors_text":"F.A. Bogomolov, Vik.S. Kulikov","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-23T09:42:13Z","title":"The ambiguity index of an equipped finite group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5763","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:72d385cce104705b0a9ff146f0b1bd4477098a265f2ebdef3ec17fe2c3618f17","target":"record","created_at":"2026-05-18T02:53:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe16c7ccd2d20049ac4590bbbafa284a5da06c8afd96a1e60081044ad2649241","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-23T09:42:13Z","title_canon_sha256":"2b78ac1fc9076faba45765c52fe5d1abb73d7345083a0ab43796ed3dec385d13"},"schema_version":"1.0","source":{"id":"1404.5763","kind":"arxiv","version":1}},"canonical_sha256":"d39a8178db1a7ef96d4a65905f29708f32b0f92550e01f5afb10818c986a1961","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d39a8178db1a7ef96d4a65905f29708f32b0f92550e01f5afb10818c986a1961","first_computed_at":"2026-05-18T02:53:28.000789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:28.000789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nbyexyAb5ibSxRg/AOPoT0f84vpKVBdm5q6W9eOEQMPEJ7wRLMDuRIJWuHztukZv6YZZ2l/Ak8pDCFsYFXlsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:28.001461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d385cce104705b0a9ff146f0b1bd4477098a265f2ebdef3ec17fe2c3618f17","sha256:f63cc365fe2451405f1558a4e758300e55fb7eaa10fb88a9d3dbc3e03b757009"],"state_sha256":"c28d7bfe759574035f5c0917b39ee28969817cb25e1ffd5e47ecd3999ad1f4b8"}